Measurement of the angle g of the Unitarity Triangle: Status and prospects

Measurement of the angle of the Unitarity Triangle:

Status and prospects

Matteo RamaLaboratori Nazionali di Frascati

Representing the BABAR Collaboration

May 25, 2007 Measurement of : Status and Prospects 2

The weak interactions of quarks

The electroweak coupling strength of the W ± to quarks is described by the elements of the Cabibbo-Kobayashi-Maskawa matrix in the Standard Model (SM)

3x3 unitary matrix ==> 4 parameters (after ad hoc choice of quark field phases)

tcuui ,,

bsdd j ,,

relative magnitudeof the elements (exp)


An irremovable complex phase in VCKM is the origin of CP violation in the SM

In the Wolfenstein parameterization:

The Cabibbo-Kobayashi-Maskawa Matrix

CPthe phase changes signin the CP-conjugated process


The Unitarity Triangle

V is unitary: VV+=1 ===>

2

3 1

in the complex plane

*

*arg ub ud

cb cd

V V

V V

=3


The BaBar Detector

Cherenkov Detector

144 quartz bars K, π, p separation

Electromagnetic Calorimeter6580 CsI crystals

e+ ID, π0 and γ reco

Drift Chamber40 layers

tracking + dE/dx

Instrumented Flux Return

12-18 layers of RPC/LST μ ID

Silicon Vertex Tracker5 layers (double-sided Si sensors)vertexing + tracking (+ dE/dx)

e+ [3.1 GeV]

e- [9 GeV]

1.5T Magnet


Pion/Kaon Discrimination: the DIRC

Cherenkov angle vs. momentum for pions and kaons

LAYOUT

>4 separationat 3 GeV/c


Key Analysis Techniques

2*2*BbeamES pEm **

beamB EEE

Background Background

(spherical)

(jet-structure)

Event topology

Signal Signal

Exploit kinematics of e+e (4S) BB for signal selection


Extraction of with BD0K

D0/D0 decay to common final stateThe interference depends on Vub and therefore on Critical parameter: ratio of amplitudes:

Select the D0 decays that enhance the interference:o 3-body (e.g. KS): Dalitz

o CP-eigen. (e.g. KS0): GLW

o DCS (e.g. D0K+-): ADS

*

*arg ub ud

cb cd

V V

V V

f

fVub

color allowed

color suppressed

1.0~)(

)(0

0

KDBA

KDBArB


The Dalitz Method


The Dalitz Method (D0KS+-)

B is strong phase diff. of A(B-D0K-) and A(B- D0K-)AD(m-

2,m+2) is the D0KS amplitude,

determined from control sampleUnknowns: rB, B and

2 2 0 2 2 2 2

2 2 0 2 2 2 2

( , ) ( ) ( , ) ( , )

( , ) ( ) ( , ) ( , )

B

B

i iD B D

i iD B D

A m m A B D K A m m r e e A m m

A m m A B D K A m m r e e A m m

2 2 0 2( )Sm m K

0 0SD K

2m

2m

0 0SD K

cbV 0SK

ubV 0SK

+

Atwood et al., PRL78, 3257 (1997)Giri et al., PRD68,054018 (2003)


The ‘Cartesian coordinates’

Goal: Fit the Dalitz plot distributions of D0KS from B- and B+ decays to extract rB, B and Complication: The Maximum Likelihood fit overestimates rB and underestimates the error of Solution: Write the Likelihood as a function of the cartesian coordinates x±, y±:

**2222Im2Re2)()(

ffyffxfyxfB

**2222Im2Re2)()(

ffyffxfyxfB

Likelihood is Gaussian and unbiased in x±, y±

),( 22 mmAf D

Strategy: Extract x±, y± from ML fit to the D0KS Dalitz plot and derive rB, B and from x±, y± with stat. procedure

)cos( BBrx )sin( BBry


The Dalitz Model of D0KS+-

From sample of 390k D0Ks (purity 98%)

Isobar Model: 16 Breit-Wigner + constant termo Parameters from PDG/other experiments (except for and ’,

fitted from data)o 8 alternative models to estimate the total systematic associated

to the model (including K-matrix to evaluate the S-wave )

K*(892)

K* DCS

(770)

0D


Sensitivity to gamma over the Dalitz plot

Sensitivity varies strongly over Dalitz plane2nd derivative of the log(L) event-by-event weighs the event

*DCS (892)K

0 *

0 *

Interference of [ ]

(suppressed) wit

A

h [ ]

DS like

B D K K

B D K K

2m

2m

2

2

ln( )d L

dweight =

22

2

1( ) ~

ln( )d L

d

*0DCS (1430)K

0 0 0SD K

events: points (weight = 1)

rB=0.12

=70°

B=180°

0 0 0

0 0 0

Interference of [ ]

with [

GLW ke

]

li

S

S

B D K K

B D K K

*DCS (892)K


Extraction of Signal

Selection of BD0K, BD*0K(D*0D00/), BD0K*

B- D*0[D0]K-B- D*0[D00]K-

B- D0K-

B- D0K*-

39823

9713 428 9312

347 106 BB

227 106 BB


Measurement of x,y

2

rB-

rB+

dB

B+

DKS Dalitz plot distribution in signal region

B-D0K- B+D0K+

B-

B+

B+

B-

B-

B+

BD0K BD*0K

BD0K*

CPVdirect 0sin2 Brd

Note: (x±,y±) of D0K,D*0K and D0K* are differentbecause (rB,dB) are different

(x±,y±) are extractedfrom the D0KS Dalitz plot


Main systematic errors

<fill>

the stat. error is dominant

syst. (no Dalitz)

syst. Dalitz model

BaBar B-D0K-

all the x,y resultsin the backup slides

Example: BD0K


From x,y to

2 1

D0

KD*0K

rb rb*

(

deg

)

(

deg

)

(5dim confidence intervals projections)

D0K* (alone)

(3dim confidence intervals projections)

1 (2))75.0( 50.0 ss krkr

hep-ex/0607104hep-ex/0507101

Doesn’t includeD0K*

(stat) (syst) (Dalitz)

Used frequentist method to extract , rB,B from (x±,y±)

347 106 BB 347 106 BB 227 106 BB


Comparison with Belle and role of rB

better precision of BaBar (x,y) does NOT translate to a smaller error on . Why?

[plots do not include Dalitz model errors]

BaBar: )9353( 15

18 Belle:

[D0K* not included])13104192(


Dependence of on the measured rB

2

B+

B-

x

y x ≈ y ≈ rB

rB

rB

(x-,y-)

(x+,y+)

~ 1/rB

the error of is ~ proportional to the uncertainty of (x,y)’s and inversely proportianal to the distance from (0,0).

Belle measurement is consistent with larger rB.


Future prospectsWith 2ab-1 (~BaBar+Belle at the end of 2008), we expect:

o 2300 BD0K; 900 BD*0K; 450 BD0K* (x,y)=0.030 (BD0K), 0.046 (BD*0K), 0.100 (BD0K*)

Difficult to predict the uncertainty on because the relative error on rb(*) is still large

o Scen1: rb(DK)=0.072; rb(D*K)=0.064; rb(DK*)=0.15: (g)~13o

o Scen 2: rb(DK)=0.098; rb(D*K)=0.104; rb(DK*)=0.24: (g)~ 9o

o Scen 3: rb(DK)=0.046; rb(D*K)=0.024; rb(DK*)=0.06: (g)~25o

Dalitz model systematics ~10o today. It’s unlikely it will ever go below ~5o using flavor-tagged D0’s. Though it may not have a major impact at the B-factories…

… it will certainly limit this measurement at the next generations of experiments! (LHCb, superB) model independent analysis

re-check numbers


Model Independent Analysis

divide the DKs Dalitz plot in 2k bins (symmetric with respect to the m+

2 vs. m-

2 axis.)express the B±DK± yields in each bin in terms of rb,,b and a total of 2k unknowns ci,si 4k equations with 2k+3 unknowns, solvable for k≥2 in principle

[Giri, Grossman, Soffer, Zupan, PRD 68, 054018 (2003)]

i

-i

][2))(( 2iiiBiDi S sycxTrTKKBd

][2))(( 2iiiBiDi S sycxTrTKKBd

for example in bin i and –i (see figure):

x±,y± usual cartesiancoordinates

i Di dmdmmmAT 22222 |),(| is measured with flavor tagged D0Ks data


Model Independent AnalysisAs a matter of fact, the 4k equations system with 2k+3 unknowns (prev. slide) requires additional input to be solvable (even at LHCb or at a SuperB).

Need to measure ci from CP-tagged D0Ks to reduce the error.

If the bin size can be chosen small enough (it depends on the BDK signal yield) it’s possible to constrain also si with

preliminary studies:~ 8o with 5000 BDK events (rB=0.1)

CLEO-c data probably not enough for LHCb precision Need BES-III data (beam collisions expected in 2007)

@ CLEO-c

21 ii cs

Y(3770)DDDCPD(KS)

hep-ph/0510246and CKM2006 WG5 session(but it implies a sufficent number of CP-tagged D)


with Model-Independent Analysis

Bondar and Poluetkov, hep-ph/0510246

()

finalize


The Method GLW


The Classic Observables

CP eigens.

CP eigens.

CP even: D0K+K-,+-

CP odd : D0KS0, KS, KS

)(2

)()(0

00

KDB

KDBKDBR CPCP

CP

2coscos21 BBB rr

)()(

)()(00

00

KDBKDB

KDBKDBA

CPCP

CPCPCP

CPBB Rr sinsin2

4 observables: RCP+, ACP+, RCP-, ACP-

RCP+ACP+ + RCP-ACP- = 0

RCP±, ACP± not independent:

selected BD0K, BD*0K, BD0K*


A Useful Alternative

Since the rB2 constraint of GLW is very weak, GLW alone can

hardly constrain gamma. But it helps when joined to Dalitz.

4

)1()1(

CPCPCPCP ARAR

x

2

2222

CPCP

b

RRyxr

Dalitz: x+, y+, x-, y-

GLW: x+, x-, rB2

Constraint (weak) of rb2

not drawn

RCP+, ACP+, RCP-, ACP- can be combined to:

The comparison with the Dalitz method is now straightforward:

Dalitz

GLW


Signal ExtractionYields are extracted with ML fit on E and the Cherenkov angleRCP± are measured as RCP±~ R±/R

(Some systematic errors cancel in the ratio)

most dangerous background sources:o charmless BK/KKK for D0/KKo interference with D0Ks(KK)non- and

Ks(0)non- for D0Ks and Ks

B±D0CP+K±

B±D0CP-K±

N(DK)=131±17

N(DK)=148±17

B±D0K±

N(DK)=1260±40

BD0K BD0 continuum+BBbar bkg

232 106 BB

PRD73 (2006) 051105


Summary of GLW Results

BaBar:Phys.Rev. D73 (2006) 051105 Phys.Rev. D71 (2005) 031102 Phys.Rev. D72 (2005) 071103

Belle:Phys.Rev. D73 (2006) 051106

BD0K

BD*0K

BD0K*


Impact of GLW and Future Prospects

Projection of errors, for various assumptions on the values of rb, at the end of 2008 (BaBar + Belle).

Dalitz (2ab-1) Dalitz+GLW (2ab-1) 13o 11o

9o 7.6o

25o 20o

1)2)3)

1) Current central values for rb (D0K + D*0K + D0K*)2) Current central values enhanced by 13) Current central values diminished by 1

numbers to be re-checked


The Method ADS


Double Cabibbo Suppressed Decays

Cons: very small BF (no signal observed yet)Pros: large bu vs. bc interference

K+-, K+-0,…

K+-, K+-0,…

)][()][(

)][()][(

KfDBKfDB

KfDBKfDBRADS

cos222 Crrrr DbDb

)][()][(

)][()][(

KfDBKfDB

KfDBKfDBAADS

ADSDb RSrr /sin2

)(/)( 002 KDKDrD = (0.060±0.002)%

S=sin(+D)C=cos(+D)

D=strong phase diff. of D0/D0K+-

D0K:


D0K

3119)( 10)13( DKADSR

(using rD=0.060±0.002)

rB<0.23 @90% CLno evidence of signal set upper limit on RADS

From RADS to rB

/

D0K+- D0K-+

RADS<0.029 @90%CL

1)

2)3)

232 106 BB

Selected BD0K, BD*0K, BD0K*. Below BD0K


D0K+-0

Compared to D0K: 3-body decay, larger BF, more background, smaller rD

If signal were abundant then a Dalitz analysis as the D0KS could be done. BUT signal is very small (actually consistent with zero)

ADS analysis:)][()][(

)][()][(

KfDBKfDB

KfDBKfDBRADS

cos222 Crrrr DbDb

)(/)( 00002 KDKDrD =(0.214±0.011)%

mdmAmdmA

mdmmmAmAC

DD

BDD

22

)()(

))()(cos()()( m = point in Dalitz Plot|C|≤1

)(),( mm = strong phases of Df and Df


D0K+-0 Results

BD0K selected with ML fit to E, mES and neural network with event shape info

signal from ML fit

RADS<0.039(95% C.L.)

Likelihood of RADS

rB<0.185(95% C.L.)

Likelihood of rB (bayesian method with flat prior for rB and |Ccos| )

D0K+-0

D0K-+0226 106 BB

preliminary preliminary

hep-ex/0607065

E(GeV)

submission to journal imminent


ADS: Summary of Results

No signal observed so far: only upper limits on rB

B-D0K-, D0K+-

B-D*0[D00]K-, D0K+-

B-D*0[D0]K-, D0K+-

B-D0K*-, D0K+-

B-D0K-, D0K+-0


B±D0K± with D0+-0


Method

First measurement of CP parameters with this channelCompared to B-D0K-, D0K0

s+-:o ~0.5 signal yield (on 324x106 BB: 170±29 vs. 398±23)o larger backgroundo different D Dalitz structureo exploits constraint of expected number of events in Likelihoodo extracts ± , ± instead of x±, y±, defined as:

cos0xx siny

2222*220 ),(),,(Re dmmdmmfmmfx

f= D Dalitz amplitude

D0+-0 DP

-=0.72±0.11±0.06

+=0.75±0.11±0.06

-=(173±42±19)o

+=(147±23±13)o


Results

this measurement alone: = 25±48 @ 68%CL* [-67,97] @ 95%CL

BDK,D0

* UTfit, bayesian procedure


sin(2+) with time-dependentCP asymmetries of B0D(*)-/


The Method

S± and C measured from time-dependent ratesBUT r too small to be extracted from C ==> r fixed using external input + SU(3) [see later]

0B 0B0

Bmixing

(*)D

(*)D

h

h+*

cbV

*cdV

udV

ubV

2 + +

2

from B0 mixing from Vub relative strong phase

)sin()cos(1),( (*)0 tmStmCthDBP dd

)sin()cos(1),( (*)0tmStmCthDBP dd

)2sin(1

22

r

rS 1

1

12

2

r

rC

)(

)((*)0

(*)0

hDBA

hDBAr ~ 0.02


Selection of signal

full reconstruction of BD+-, D*+-, D+-

partial reconstruction of BD*+- (in D*+D0+, D0 is NOT reconstructed)

18710±270Pur~50%

70580±660Pur~30%

lepton tag

kaon tag

all tagsBD+-

BD*+-

BD+-

mmiss = missing mass of D0

high purity very high reco. efficiencylower purity (B tag-dependent)only B0D*

232 106 BB

232 106 BB


Fit to the Time-dependent Rates

Since the CP asym. of signal is small, the effect of bu vs. bc interference in the Btag must be taken into account. Introduction of CPV parameters of the tag side (r’, ’)

t (ps)

Brec=D*-+

Btag=B0

Brec=D*-+

Btag=B0bar

Brec=D*+-

Btag=B0

Brec=D*+-

Btag=B0bar

full reco, lepton tag partial reco, lepton tag

-10 -1010 10

bcaS

=±1 for )hD (*)

a,b,c measured from time-dep fit. a,c used to constrain 2+0 with lepton tag


The Results

full reco partial reco)tan(

)(

)(

(*)

(*)(*)

(*)0

(*)0

C

D

DshD

sf

f

hDBBF

hDBBFr

•neglects exchange diagrams, •uses fD/fDs to take into account SU(3) break. •assumes factorization (a 30% relative error to these assumptions is applied)

BaBar full reco + partial reco

|sin(2+)|>0.64 (0.40) @ 68% (90%) CL

results from the time-dep fit estimation of rD(*)h

see also Baak’s talkat CKM2006

BaBar+Belle

2+ = -90±33


Other Methods


B0D(*)0K(*)0

Interesting channel for the future. o Can measure using B0D0K*0 vs. B0D0K*0 (K*0K+-

self-tagging) as B-D0K-

o Can measure sin(2+) using time-dep B0D0KS0

expected large rB (naïve estimate: rB ~ 0.4)

4.0)( 0*0 KDrB @90% CL

From

using bayesian procedure

still too few sig. events for time-dep analysis

constraining with B0D(*)0K(*)0 could be harder than originally hoped


Combination

o1926 )78(

Babar + Belle Babar + Belle

o)1983(


with 1ab-1 and beyond

possibly to be replaced with new one


Summary


End


Likelihood used to extract signal yields and x,y


x,y results of BD(*)0K(*), D0Ks

BaBar

Bellehep-ex/0604054

hep-ex/0507101hep-ex/0607104BD0K*

BB 10386 6

BB 10347 6

BB 10227 6


BD0K

BD*0[D00]K

BD*0[D0]K

B- B+

BaBar: signal-enhancedDalitz distributions

B- B+BD0K*


B- B+

BD0K

BD*0[D00]K

BD0K*

Belle: signal-enhancedDalitz distributions


constraints on rBD0K D*0K D0K*

rB(DK)=0.071±0.024 rB(D*K)=0.066±0.042 rB(DK*)=0.15±0.09


effect of D0 mixing in BD0K

Measurement of the angle g of the Unitarity Triangle: Status and prospects

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Transcript of Measurement of the angle g of the Unitarity Triangle: Status and prospects